I am not an HVAC tech/plumber but I can tell you, if there is any doubt about a thermocouple an HVAC tech is going to replace. Because once you have it out to test you might as well replace as all the labor has been done and your chances of a new one being defective or working intermittently is low and due to many factors there is a limited life expectancy of a thermocouple.
I found a very thorough article on Thermocouples as I was researching this for you:
http://www.marlinmfg.com/tcfundamentals.pdf
The testing of a thermocouple in place is on page 14.
As stated I am not an HVAC tech, however I have changed a thermocouple and it was simple and required basic tools.
This is very similar to what I had:
http://www.americanwaterheater.com/support/manuals/nat_tc_instr.pdf
Once you have it changed this article on lighting and adjusting a furnace pilot will work for the water heater as well:
These adjustments will work for your water heater:
http://discussions.tommmymac.us/HowTo_Library/Service_a_Gas_Furnace-Subject_HVAC_Furnace-F2226.html
Greg
Webmaster
Winter Park Homes for Sale